MAYBE
Time: 0.063305
TRS:
 {                 f X -> cons(X, n__f n__g X),
                   f X -> n__f X,
                   g X -> n__g X,
                 g s X -> s s g X,
                 g 0() -> s 0(),
  sel(s X, cons(Y, Z)) -> sel(X, activate Z),
  sel(0(), cons(X, Y)) -> X,
            activate X -> X,
       activate n__f X -> f activate X,
       activate n__g X -> g activate X}
 DP:
  DP:
   {               g# s X -> g# X,
    sel#(s X, cons(Y, Z)) -> sel#(X, activate Z),
    sel#(s X, cons(Y, Z)) -> activate# Z,
         activate# n__f X -> f# activate X,
         activate# n__f X -> activate# X,
         activate# n__g X -> g# activate X,
         activate# n__g X -> activate# X}
  TRS:
  {                 f X -> cons(X, n__f n__g X),
                    f X -> n__f X,
                    g X -> n__g X,
                  g s X -> s s g X,
                  g 0() -> s 0(),
   sel(s X, cons(Y, Z)) -> sel(X, activate Z),
   sel(0(), cons(X, Y)) -> X,
             activate X -> X,
        activate n__f X -> f activate X,
        activate n__g X -> g activate X}
  UR:
   {            f X -> cons(X, n__f n__g X),
                f X -> n__f X,
                g X -> n__g X,
              g s X -> s s g X,
              g 0() -> s 0(),
         activate X -> X,
    activate n__f X -> f activate X,
    activate n__g X -> g activate X,
            a(x, y) -> x,
            a(x, y) -> y}
   EDG:
    {(sel#(s X, cons(Y, Z)) -> activate# Z, activate# n__g X -> activate# X)
     (sel#(s X, cons(Y, Z)) -> activate# Z, activate# n__g X -> g# activate X)
     (sel#(s X, cons(Y, Z)) -> activate# Z, activate# n__f X -> activate# X)
     (sel#(s X, cons(Y, Z)) -> activate# Z, activate# n__f X -> f# activate X)
     (activate# n__f X -> activate# X, activate# n__g X -> activate# X)
     (activate# n__f X -> activate# X, activate# n__g X -> g# activate X)
     (activate# n__f X -> activate# X, activate# n__f X -> activate# X)
     (activate# n__f X -> activate# X, activate# n__f X -> f# activate X)
     (activate# n__g X -> g# activate X, g# s X -> g# X)
     (activate# n__g X -> activate# X, activate# n__f X -> f# activate X)
     (activate# n__g X -> activate# X, activate# n__f X -> activate# X)
     (activate# n__g X -> activate# X, activate# n__g X -> g# activate X)
     (activate# n__g X -> activate# X, activate# n__g X -> activate# X)
     (g# s X -> g# X, g# s X -> g# X)
     (sel#(s X, cons(Y, Z)) -> sel#(X, activate Z), sel#(s X, cons(Y, Z)) -> sel#(X, activate Z))
     (sel#(s X, cons(Y, Z)) -> sel#(X, activate Z), sel#(s X, cons(Y, Z)) -> activate# Z)}
    STATUS:
     arrows: 0.673469
     SCCS (3):
      Scc:
       {sel#(s X, cons(Y, Z)) -> sel#(X, activate Z)}
      Scc:
       {activate# n__f X -> activate# X,
        activate# n__g X -> activate# X}
      Scc:
       {g# s X -> g# X}
      
      SCC (1):
       Strict:
        {sel#(s X, cons(Y, Z)) -> sel#(X, activate Z)}
       Weak:
       {                 f X -> cons(X, n__f n__g X),
                         f X -> n__f X,
                         g X -> n__g X,
                       g s X -> s s g X,
                       g 0() -> s 0(),
        sel(s X, cons(Y, Z)) -> sel(X, activate Z),
        sel(0(), cons(X, Y)) -> X,
                  activate X -> X,
             activate n__f X -> f activate X,
             activate n__g X -> g activate X}
       Open
      
      SCC (2):
       Strict:
        {activate# n__f X -> activate# X,
         activate# n__g X -> activate# X}
       Weak:
       {                 f X -> cons(X, n__f n__g X),
                         f X -> n__f X,
                         g X -> n__g X,
                       g s X -> s s g X,
                       g 0() -> s 0(),
        sel(s X, cons(Y, Z)) -> sel(X, activate Z),
        sel(0(), cons(X, Y)) -> X,
                  activate X -> X,
             activate n__f X -> f activate X,
             activate n__g X -> g activate X}
       Open
      
      SCC (1):
       Strict:
        {g# s X -> g# X}
       Weak:
       {                 f X -> cons(X, n__f n__g X),
                         f X -> n__f X,
                         g X -> n__g X,
                       g s X -> s s g X,
                       g 0() -> s 0(),
        sel(s X, cons(Y, Z)) -> sel(X, activate Z),
        sel(0(), cons(X, Y)) -> X,
                  activate X -> X,
             activate n__f X -> f activate X,
             activate n__g X -> g activate X}
       Open